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# Copyright 2018 Kornia Team
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"""nn.Module for the projection of points in the canonical z=1 plane."""

# inspired by: https://github.com/farm-ng/sophus-rs/blob/main/src/sensor/perspective_camera.rs
from __future__ import annotations

from typing import Optional

import torch

from kornia.core.check import KORNIA_CHECK_SHAPE


def project_points_z1(points_in_camera: torch.Tensor) -> torch.Tensor:
    r"""Project one or more points from the camera frame into the canonical z=1 plane through perspective division.

    .. math::

        \begin{bmatrix} u \\ v \\ w \end{bmatrix} =
        \begin{bmatrix} x \\ y \\ z \end{bmatrix} / z

    .. note::

        This function has a precondition that the points are in front of the camera, i.e. z > 0.
        If this is not the case, the points will be projected to the canonical plane, but the resulting
        points will be behind the camera and causing numerical issues for z == 0.

    Args:
        points_in_camera: torch.Tensor representing the points to project with shape (..., 3).

    Returns:
        torch.Tensor representing the projected points with shape (..., 2).

    Example:
        >>> points = torch.tensor([1., 2., 3.])
        >>> project_points_z1(points)
        tensor([0.3333, 0.6667])

    """
    KORNIA_CHECK_SHAPE(points_in_camera, ["*", "3"])
    return points_in_camera[..., :2] / points_in_camera[..., 2:3]


def unproject_points_z1(
    points_in_cam_canonical: torch.Tensor, extension: Optional[torch.Tensor] = None
) -> torch.Tensor:
    r"""Unproject one or more points from the canonical z=1 plane into the camera frame.

    .. math::
        \begin{bmatrix} x \\ y \\ z \end{bmatrix} =
        \begin{bmatrix} u \\ v \end{bmatrix} \cdot w

    Args:
        points_in_cam_canonical: torch.Tensor representing the points to unproject with shape (..., 2).
        extension: torch.Tensor representing the extension (depth) of the points to unproject with shape (..., 1).

    Returns:
        torch.Tensor representing the unprojected points with shape (..., 3).

    Example:
        >>> points = torch.tensor([1., 2.])
        >>> extension = torch.tensor([3.])
        >>> unproject_points_z1(points, extension)
        tensor([3., 6., 3.])

    """
    KORNIA_CHECK_SHAPE(points_in_cam_canonical, ["*", "2"])

    if extension is None:
        extension = torch.ones(
            points_in_cam_canonical.shape[:-1] + (1,),
            device=points_in_cam_canonical.device,
            dtype=points_in_cam_canonical.dtype,
        )  # (..., 1)
    elif extension.shape[0] > 1:
        extension = extension[..., None]  # (..., 1)

    return torch.cat([points_in_cam_canonical * extension, extension], dim=-1)


def dx_project_points_z1(points_in_camera: torch.Tensor) -> torch.Tensor:
    r"""Compute the derivative of the x projection with respect to the x coordinate.

    Returns point derivative of inverse depth point projection with respect to the x coordinate.

    .. math::
        \frac{\partial \pi}{\partial x} =
        \begin{bmatrix}
            \frac{1}{z} & 0 & -\frac{x}{z^2} \\
            0 & \frac{1}{z} & -\frac{y}{z^2}
        \end{bmatrix}

    .. note::
        This function has a precondition that the points are in front of the camera, i.e. z > 0.
        If this is not the case, the points will be projected to the canonical plane, but the resulting
        points will be behind the camera and causing numerical issues for z == 0.

    Args:
        points_in_camera: torch.Tensor representing the points to project with shape (..., 3).

    Returns:
        torch.Tensor representing the derivative of the x projection with respect to the x coordinate
        with shape (..., 2, 3).

    Example:
        >>> points = torch.tensor([1., 2., 3.])
        >>> dx_project_points_z1(points)
        tensor([[ 0.3333,  0.0000, -0.1111],
                [ 0.0000,  0.3333, -0.2222]])

    """
    KORNIA_CHECK_SHAPE(points_in_camera, ["*", "3"])

    x = points_in_camera[..., 0]
    y = points_in_camera[..., 1]
    z = points_in_camera[..., 2]

    z_inv = 1.0 / z
    z_sq = z_inv * z_inv
    zeros = torch.zeros_like(z_inv)
    return torch.stack(
        [
            torch.stack([z_inv, zeros, -x * z_sq], dim=-1),
            torch.stack([zeros, z_inv, -y * z_sq], dim=-1),
        ],
        dim=-2,
    )
